# Magnetic energy

Corresponding Wikipedia article: Magnetic energy

The magnetic interaction of the aetheric vortices is the magnetic force ("Magnetism", 7 and 8) effect, which manifests the interaction potential energy, which tends to its minimum.

It can be written similar to the equation ("Magnetism", 4): $grad\frac{\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}}{2}=(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{H}}+\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{H}}\tag{1}$ The $$(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{H}}$$ component produces the electric field, and it is zero for the magnetic field. The $$(\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{H}})$$ component is the magnetic force within matter.

SI CGS Simplified $$\tag{2}$$ $w_B=\frac{\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}}{2}=\frac{|\mathbf{\overrightarrow{B}}|^2}{2\mu_0 \mu}$ $w_B=\frac{\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}}{8\pi}=\frac{|\mathbf{\overrightarrow{B}}|^2}{8\pi\mu}$ $w_B=\frac{\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}c^2}{2}=\frac{|\mathbf{\overrightarrow{B}}|^2c}{2\mu}$

Let the first source has the field $$\mathbf{\overrightarrow{B_1}}$$ and $$\mathbf{\overrightarrow{H_1}}$$, and the second has $$\mathbf{\overrightarrow{B_2}}$$ and $$\mathbf{\overrightarrow{H_2}}$$. Then the equation of full energy is: $\frac{(\mathbf{\overrightarrow{B_1}}+\mathbf{\overrightarrow{B_2}})(\mathbf{\overrightarrow{H_1}}+\mathbf{\overrightarrow{H_2}})}{2}=\frac{\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_1}}}{2}+\frac{\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_2}}+\mathbf{\overrightarrow{B_2}}\mathbf{\overrightarrow{H_1}}}{2}+\frac{\mathbf{\overrightarrow{B_2}}\mathbf{\overrightarrow{H_2}}}{2}\tag{3}$ Here $$\frac{\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_1}}}{2}$$ and $$\frac{\mathbf{\overrightarrow{B_2}}\mathbf{\overrightarrow{H_2}}}{2}$$ are the densities of own energy for the first and the second source separately. The interaction energy density with certain permeability $$\mu$$ at the given point has few identical representations: $\frac{\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_2}}+\mathbf{\overrightarrow{B_2}}\mathbf{\overrightarrow{H_1}}}{2}=\mu_0\mu\mathbf{\overrightarrow{H_1}}\mathbf{\overrightarrow{H_2}}=\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_2}}=\mathbf{\overrightarrow{H_1}}\mathbf{\overrightarrow{B_2}}\tag{4}$ Thus the potential energy volumetric density of the magnetic interaction is: $w=\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}\tag{5}$

Example. The inductive coil has the field energy of density $$\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}/2$$ and interacts with the magnetized core with the energy density $$\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}$$, which produces the heat losses.

Two magnetic object (which have a magnetic field) are mutually attracted by their poles by some way, which provides the minimal energy of the resulting field:

Attraction of poles Examples
different Solid bodies (magnets). Rarely the elementary particles.
same Pairs of elementary particles, the covalent bonds or the Cooper pairs.